TCM is based predominantly on Daoist philosophy while TM is based on Buddhist and has more similarities with ayurvedic medicine.

"But if you know how to observe yourself, you will discover your real nature, the primordial state, the state of Guruyoga, and then all will become clear because you will have discovered everything"-Namkhai Norbu Rinpoche

Several summers ago, I spent a couple of weeks at H.H. Kusum Lingpa's Lung Ngon monastery in Golok. There was a small clinic in the monastery. Seeing both Tibetan and Chinese medicines in the dispensary, I asked the Tibetan doctor staffing the clinic about the use of both Chinese and Tibetan medicines and he said both are effective and that he prescribed both. In questioning further, I tried to find out if he was prescribing Chinese medicine based on Chinese medical pattern discrimination, but it appeared that he was prescribing the Chinese medicines based on disease diagnosis from the information on the medicines' packaging. In any case, he thought both medicines were safe, effective, and compatible. What it seemed to me is that, if he had a Chinese ready-made medicine on hand that he thought would be effective for a patient's condition, he was happy to prescribe that. Cheap, easy to take, portable, storable, and easily available. In any case, he didn't seem to have any particular prejudice towards Chinese meds.

IME as a doctor of Chinese medicine (retired), many Tibetan Lamas are happy to use both Chinese and Tibetan medicines. Because many Tibetan Lamas have Chinese students, many of them are regularly given Chinese meds by their disciples. I once had to go through all the Chinese meds given to Kyabje Chatral Rinpoche to decide which ones might be useful for Him and which ones were off the mark (in terms of Chinese medical pattern discrimination). No one in His household could read the Chinese. Also, many Tibetan Lamas and laypersons alike like to get Chinese acupuncture. When my wife and I volunteered at the Shechen Clinic in Boudha for a couple of years, our clinic was the most popular in the compound. We always had the longest line of patients; more than the Tibetan or Western docs or the homeopath.